Cutting insert, cutting tool, and method for manufacturing machined product

ABSTRACT

A cutting insert may include an upper surface, a lower surface, a front lateral surface and a rear lateral surface. The upper surface may include a first upper cutting edge and an upper constraining surface. The lower surface may include a lower constraining surface. The lower constraining surface may include a lower groove. The lower groove may include a first region, a second region and a third region. The first region may be located on a side opposite to the upper constraining surface. A wedge angle of the first region may be a first angle, a wedge angle of the second region may be a second angle, and a wedge angle of the third region may be a third angle. The first angle may be smaller than each of the second angle and the third angle.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a national stage entry according to 35 U.S.C. 371 ofPCT Application No. PCT/JP2020/007408, filed on Feb. 25, 2020, whichclaims priority to Japanese Application No. 2019-032493, filed Feb. 26,2019, which are entirely incorporated herein by reference.

FIELD OF INVENTION

The present disclosure may relate to a cutting insert for use in acutting process. Specifically, the present disclosure may relate to arotary tool for use in a turning process, such as grooving process.

TECHNICAL BACKGROUND

For example, a cutting tip is discussed in Japanese Unexamined PatentApplication Publication No. 2011-520630 (Patent Document 1) as a cuttinginsert for use in a turning process of a workpiece, such as metal. Thecutting tip (cutting insert) discussed in Patent Document 1 may includean upper surface, a lower surface and a peripheral lateral surface. Theperipheral lateral surface may include a front end surface and a rearend surface. The lower surface may include a constraining surface in theshape of a V-shaped groove extended along a central axis (verticalaxis). The constraining surface may include a first surface componentlocated on a side of the front end surface, and a second surfacecomponent located on a side of the rear end surface. A wedge angle inthe second surface component may be smaller than a wedge angle in thefirst surface component.

In cases where a cutting process is carried out using the cutting insertdiscussed in Patent Document 1, cutting load due to a principal force inthe cutting process may also tend to be transmitted to the secondsurface component because the second surface component is located on theside of the rear end surface. Durability of the cutting insert may belowered in the second surface component because the wedge angle in thesecond surface component is relatively small.

SUMMARY

A cutting insert in a non-limiting aspect of the present disclosure mayinclude an upper surface, a lower surface, a front lateral surface and arear lateral surface. The lower surface may be located on a sideopposite to the upper surface. The front lateral surface may be locatedbetween the upper surface and the lower surface. The rear lateralsurface may be located between the upper surface and the lower surface,and may be located on a side opposite to the front lateral surface. Theupper surface may include a first upper cutting edge and an upperconstraining surface. The first upper cutting edge may be located on anintersection with the front lateral surface. The upper constrainingsurface may be located closer to the rear lateral surface than the firstupper cutting edge, and may be contactable with a holder. The lowersurface may include a lower constraining surface contactable with theholder. The lower constraining surface may include a lower groove havinga V-shape extended from a region located near the front lateral surfacetoward the rear lateral surface. The lower groove may include a firstregion, a second region and a third region. The first region may belocated on a side opposite to the upper constraining surface. The secondregion may be located closer to the front lateral surface than the firstregion. The third region may be located closer to the rear lateralsurface than the first region. A wedge angle of the first region may bea first angle, a wedge angle of the second region may be a second angle,and a wedge angle of the third region may be a third angle in a crosssection orthogonal to an extending direction of the lower groove. Thefirst angle may be smaller than each of the second angle and the thirdangle.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view illustrating a cutting insert in anon-limiting embodiment;

FIG. 2 is a plan view of the cutting insert illustrated in FIG. 1 asviewed from a side of an upper surface;

FIG. 3 is a plan view of the cutting insert illustrated in FIG. 1 asviewed from a side of a lower surface;

FIG. 4 is a plan view of the cutting insert illustrated in FIG. 2 asviewed from a side of a front lateral surface;

FIG. 5 is a plan view of the cutting insert illustrated in FIG. 2 asviewed from a side of a rear lateral surface;

FIG. 6 is a side view of the cutting insert illustrated in FIG. 2 asviewed from an A1 direction;

FIG. 7 is a cross-sectional view taken along the line VII-VII in thecutting insert illustrated in FIG. 6;

FIG. 8 is a cross-sectional view taken along the line VIII-VIII in thecutting insert illustrated in FIG. 6;

FIG. 9 is a cross-sectional view taken along the line IX-IX in thecutting insert illustrated in FIG. 6;

FIG. 10 is a cross-sectional view taken along the line X-X in thecutting insert illustrated in FIG. 6;

FIG. 11 is a perspective view illustrating a cutting tool in anon-limiting embodiment;

FIG. 12 is an enlarged view of a region B1 illustrated in FIG. 11;

FIG. 13 is a schematic diagram illustrating one of steps in a method formanufacturing a machined product in a non-limiting embodiment;

FIG. 14 is a schematic diagram illustrating one of the steps in themethod for manufacturing a machined product in the non-limitingembodiment;

FIG. 15 is a schematic diagram illustrating one of the steps in themethod for manufacturing a machined product in the non-limitingembodiment; and

FIG. 16 is a schematic diagram illustrating one of the steps in themethod for manufacturing a machined product in the non-limitingembodiment.

DETAILED DESCRIPTION

<Inserts>

Cutting inserts 1 (hereinafter also referred to simply as “inserts 1”)in non-limiting embodiments of the present disclosure may be describedin detail below with reference to the drawings. For the sake ofdescription, the drawings referred to in the following may illustrate,in simplified form, only main members necessary for describing theembodiments. The cutting inserts 1 may therefore be capable of includingany arbitrary structural member not illustrated in the drawings referredto. Dimensions of the members in each of the drawings may faithfullyrepresent neither dimensions of actual structural members nordimensional ratios of these members.

The insert 1 may include an upper surface 3, a lower surface 5, a frontlateral surface 7 and a rear lateral surface 9. The lower surface 5 maybe located on a side opposite to the upper surface 3. The front lateralsurface 7 and the rear lateral surface 9 may be individually locatedbetween the upper surface 3 and the lower surface 5. In this case, therear lateral surface 9 may be located on a side opposite to the frontlateral surface 7. The front lateral surface 7 and the rear lateralsurface 9 may individually connect to the upper surface 3 and the lowersurface 5.

In addition to these surfaces, the insert 1 may include a first lateralsurface 11 and a second lateral surface 13. The first lateral surface 11and the second lateral surface 13 may be located between the uppersurface 3 and the lower surface 5 and between the front lateral surface7 and the rear lateral surface 9. In this case, the first lateralsurface 11 and the second lateral surface 13 may individually connect tothe upper surface 3, the lower surface 5, the front lateral surface 7and the rear lateral surface 9.

The insert 1 may have a quadrangular prism shape including the uppersurface 3, the lower surface 5, the front lateral surface 7, the rearlateral surface 9, the first lateral surface 11 and the second lateralsurface 13 as illustrated in FIG. 1. The insert 1 may have a prism shapeextended along a central axis O1 from a front end to a rear end as in anembodiment illustrated in FIG. 1.

The front lateral surface 7 may be located at the front end, and therear lateral surface 9 may be located at the rear end. As in theembodiment illustrated in FIG. 1, the front lateral surface 7 and therear lateral surface 9 may have a quadrangular shape, and the foursurfaces of the upper surface 3, the lower surface 5, the first lateralsurface 11 and the second lateral surface 13 may be individuallyextended from the front lateral surface 7 toward the rear lateralsurface 9.

Each of the upper surface 3, the lower surface 5, the front lateralsurface 7, the rear lateral surface 9, the first lateral surface 11 andthe second lateral surface 13 is not limited to specific dimensions. Forexample, a length of the upper surface 3 in a direction along thecentral axis O1 in a front view (top view) of the upper surface 3 may beset to approximately 3-50 mm. A length of the upper surface 3 in adirection orthogonal to the central axis O1 in a top view may be set toapproximately 1.5-15 mm. A height of the insert 1 indicated by adistance between the upper surface 3 and the lower surface 5 may be setto approximately 2-20 mm.

The upper surface 3 may include a first upper cutting edge 15 and anupper constraining surface 17. The first upper cutting edge 15 may belocated on an intersection with the front lateral surface 7 on the uppersurface 3. The first upper cutting edge 15 may be located all over theintersection of the upper surface 3 and the front lateral surface 7, ormay be located only a part of the intersection of the upper surface 3and the front lateral surface 7. The first upper cutting edge 15 may beused for cutting out a workpiece. The first upper cutting edge 15 in theembodiment illustrated in FIG. 1 may generally be called a front cuttingedge or main cutting edge.

The upper constraining surface 17 may be located closer to the rearlateral surface 9 than the first upper cutting edge 15. The upperconstraining surface 17 may be contactable with a holder when the insert1 is attached to the holder. The upper constraining surface 17 mayinclude an end part on a side of the rear end on the upper surface 3,namely, an intersection with the rear lateral surface 9, or may belocated away from the intersection.

The upper surface 3 may include a rake surface 19 located along thefirst upper cutting edge 15. The rake surface 19 may connect to theupper constraining surface 17, or may be located away from the upperconstraining surface 17. The upper surface 3 may further include, as acutting edge, a second upper cutting edge 21 in addition to the firstupper cutting edge 15.

The second upper cutting edge 21 may be located on an intersection withthe first lateral surface 11 on the upper surface 3, or an intersectionwith the second lateral surface 13 on the upper surface 3. For example,the second upper cutting edge 21 may be located on an intersection withthe first lateral surface 11 on the upper surface 3, and on anintersection with the second lateral surface 13 on the upper surface 3as illustrated in FIG. 1.

The lower surface 5 may include a lower constraining surface 23. Thelower constraining surface 23 may be located all over the lower surface5 or only a part of the lower surface 5. The lower constraining surface23 may be contactable with the holder when the insert 1 is attached tothe holder. The insert 1 can be held by the holder by bringing the lowerconstraining surface 23 and the upper constraining surface 17 intocontact with the holder.

The lower constraining surface 23 may include a lower groove 25 extendedfrom a region located near the front lateral surface 7 toward the rearlateral surface 9. The lower groove 25 may open into the front lateralsurface 7 or may be located away from the front lateral surface 7.Similarly, the lower groove 25 may open into the rear lateral surface 9or may be located away from the rear lateral surface 9. The lower groove25 may be located away from the front lateral surface 7 and the rearlateral surface 9 as in an embodiment illustrated in FIG. 3.

In other words, the lower groove 25 may be extended parallel to thecentral axis O1 because the lower groove 25 is extended from a side ofthe front lateral surface 7 toward a side of the rear lateral surface 9in the embodiment illustrated in FIG. 3. The lower groove 25 may have aV-shape in a cross section orthogonal to an extending direction thereof,namely, a cross section orthogonal to the central axis O1.

As used herein, the phrase that the lower groove 25 has the V-shape maydenote that the lower groove 25 includes a pair of inclined surfaces 27having a larger distance therebetween as going away from a bottom of thelower surface 25. Therefore, for example, a concave curved surface 29 toconnect the pair of inclined surfaces 27 may be located on the bottom ofthe lower groove 25.

The lower groove 25 may include a first region 31, a second region 33and a third region 35. The first region 31 may be located on a sideopposite to the upper constraining surface 17. The second region 33 maybe located closer to the front lateral surface 7 than the first region31. The second region 33 may include an end portion on a side of thefront lateral surface 7, or may be located away from the front lateralsurface 7. The third region 35 may be located closer to the rear lateralsurface 9 than the first region 31. The third region 35 may include anend part on a side of the rear lateral surface 9, or may be located awayfrom the rear lateral surface 9.

The first region 31, the second region 33 and the third region 35 mayhave a V-shape. A comparison may be made of shapes of the first region31, the second region 33 and the third region 35 in a cross sectionorthogonal to the extending direction of the lower groove 25, namely,the cross section orthogonal to the central axis O1. Specifically, awedge angle of the first region 31 may be a first angle θ1, a wedgeangle of the second region 33 may be a second angle θ2, and a wedgeangle of the third region 35 may be a third angle θ3 in the crosssection orthogonal to the extending direction of the lower groove 25.

As used herein, the term “wedge angle” may denote an angle formed by thepair of inclined surfaces 27 in the cross section orthogonal to thecentral axis O1. That is, the wedge angle of the lower groove 25 in across section which is orthogonal to the central axis O1 and passesthrough the first region 31 may be the first angle θ1. The wedge angleof the lower groove 25 in a cross section which is orthogonal to thecentral axis O1 and passes through the second region 33 may be thesecond angle θ2. The wedge angle of the lower groove 25 in a crosssection which is orthogonal to the central axis O1 and passes throughthe third region 35 may be the third angle θ3. The wedge angle in theV-shaped groove may also be called an opening angle.

The first angle θ1 may be smaller than each of the second angle θ2 andthe third angle θ3. This may lead to enhanced durability of the insert1. Because the first angle θ1 is relatively small, the insert 1 may beless susceptible to positional deviation in the direction orthogonal tothe central axis O1 in a top view.

If the second angle θ2 and the third angle θ3 are relatively large,principal force applied to the insert 1 during the cutting process maytend to be received by the second region located on a side of the frontlateral surface 7 and the third region 35 located on the side of therear lateral surface 9. Because the principal force tends to be receivedby the second region 33 and the third region 35, the principal force maybe less likely to be applied to the first region 31 located betweenthese regions. The insert 1 may therefore have enhanced durability.

The first angle θ1, the second angle θ2 and the third angle θ3 are notlimited to a specific value. The first angle θ1 may be set to, forexample, 100-140°. The second angle θ2 may be set to, for example,120-160°. The third angle θ3 may be set to, for example, 120-160°.

The first angle θ1, the second angle θ2 and the third angle θ3 may bekept constant or changed. For example, the first angle θ1 may be changedand the second angle θ2 and the third angle θ3 may be kept constant.Specifically, the first region 31 may include a first part 37 which islocated on a side of the front lateral surface 7 and whose wedge angleincreases as coming closer to the rear lateral surface 9, and a secondpart 39 which is located on a side of the rear lateral surface 9 andwhose wedge angle increases as coming closer to the front lateralsurface 7.

If the first region 31 includes the first part 37, it may be easy toavoid a sharp change in wedge angle at a boundary between the firstregion 31 and the second region 33. If the first region 31 includes thesecond part 39, it may be easy to avoid a sharp change in wedge angle ata boundary between the first region 31 and the third region 35. Theinsert 1 may therefore have further enhanced durability.

If the second angle θ2 is kept constant, the pair of inclined surfaces27 in the second region 33 may have a planar shape. In this case, thesecond region 33 may tend to be brought into surface-to-surface contactwith the holder. Similarly, if the third angle θ3 is kept constant, thepair of inclined surfaces 27 in the third region 35 may have a planarshape. In this case, the third region 35 may tend to be brought intosurface-to-surface contact with the holder. In this case, the principalforce further may tend to be received by the second region 33 and thethird region 35.

If the first angle θ1, the second angle θ2 and the third angle θ3 arechanged, their respective maximum values may be compared with oneanother.

The second angle θ2 may be equal to or smaller than the third angle θ3.The second angle θ2 may be smaller than the third angle θ3 in anembodiment illustrated in FIGS. 8 and 9. The second region 33 may belocated closer to the front lateral surface 7 than the first region 31and the third region 35. Specifically, the second region 33 may belocated closer to the first upper cutting edge 15 than the first region31 and the third region 35.

If the second angle θ2 in the second region 33 located near the firstupper cutting edge 15 subjected to cutting load during the cuttingprocess is smaller than the third angle θ3, the insert 1 may be lesssusceptible to positional deviation in the direction orthogonal to thecentral axis O1 in a top view.

The upper constraining surface 17 may include an upper groove 41extended from a region located near the front lateral surface 7 towardthe rear lateral surface 9. The upper groove 41 may open into the frontlateral surface 7, or may be located away from the front lateral surface7. Similarly, the upper groove 41 may open into the rear lateral surface9, or may be located away from the rear lateral surface 9.

In other words, the upper groove 41 may be extended parallel to thecentral axis O1 because the upper groove 41 is extended from a side ofthe front lateral surface 7 toward a side of the rear lateral surface 9in the embodiment illustrated in FIG. 3. The upper groove 41 may have aV-shape in a cross section orthogonal to an extending direction thereof,namely, a cross section orthogonal to the central axis O1. That is, theupper groove 41 may include a pair of inclined surfaces 27 having alarger distance therebetween as going away from a bottom of the uppergroove 41.

If the upper constraining surface 17 includes the upper groove 41, theinsert 1 can be stably held by the holder. Particularly, if the uppergroove 41 is extended parallel to the lower groove 25, the insert 1 canbe further stably held by the holder.

In cases where the upper groove 41 has the V-shape as in an embodimentillustrated in FIG. 10, a wedge angle of the upper groove 41 may be afourth angle θ4. In this case, the first angle θ1 may be equal to orsmaller than the fourth angle θ4. If the first angle θ1 is smaller thanthe fourth angle θ4, namely, if the fourth angle θ4 is larger than thefirst angle θ1, the insert 1 may have further enhanced durability. Itmay be possible to reduce the probability that cracks occur from abottom of the upper groove 41 to a bottom of the lower groove 25, whilehaving a relatively small value of the first angle θ1.

The insert 1 can be stably held by the holder in cases where at leastparts in portions located on opposite sides of the upper groove 41 andthe lower groove 25 have the same wedge angle. For example, the thirdregion 35 may include a first portion 43 located on a side opposite tothe upper constraining surface 17, and the third angle θ3 at the firstportion 43 may be equal to the fourth angle θ4.

The term “having the same angle” may denote that the two angles may notbe strictly the same. If a difference between the two angles is as smallas approximately 2°, these two angles may be regarded as being the same.

As described earlier, the concave curved surface 29 that connects thepair of inclined surfaces 27 may be located on the bottom of the lowergroove 25. For example, a bottom having a concave curved surface shapein the first region 31 may be a first bottom part 29 a, and the pair ofinclined surfaces 27 in the first region 31 may be first inclinedsurfaces 27 a. That is, the first region 31 may include the first bottompart 29 a having the concave curved surface shape, and the firstinclined surfaces 27 a that are flat and connect to the first bottompart 29 a along an extending direction of the lower groove 25.

A width of the first bottom part 29 a in the extending direction of thelower groove 25 may be a first width W1, and a width of each of thefirst inclined surfaces 27 a in the extending direction of the lowergroove 25 may be a second width W2. In this case, a maximum value of thefirst width W1 may be smaller than a maximum value of the second widthW2. With this configuration, the insert 1 may be much less prone topositional deviation in the direction orthogonal to the central axis O1in a top view.

For example, a bottom having a concave curved surface shape in thesecond region 33 may be a second bottom part 29 b, and the pair ofinclined surfaces 27 in the second region 33 may be second inclinedsurfaces 27 b. That is, the second region 33 may include the secondbottom part 29 b having the concave curved surface shape, and the secondinclined surfaces 27 b that are flat and connect to the second bottompart 29 b along the extending direction of the lower groove 25.

A width of the second bottom part 29 b in the extending direction of thelower groove 25 may be a third width W3, and a width of each of thesecond inclined surfaces 27 b in the extending direction of the lowergroove 25 may be a fourth width W4. In this case, a maximum value of thethird width W3 may be larger than a maximum value of the fourth widthW4. This may lead to enhanced durability of the second region 33.

For example, inorganic materials, such as cemented carbide, cermet andceramics, may be usable as a material of the insert 1. Examples ofcomposition of the cemented carbide may include WC (tungstencarbide)-Co, WC—TiC (titanium carbide)-Co and WC—TiC—TaC (tantalumcarbide)-Co, in which WC, TiC and TaC may be hard particles and Co maybe a binding phase.

The cermet may be a sintered composite material obtainable bycompositing metal into a ceramic component. Examples of the cermet mayinclude compounds composed mainly of TiC or TiN (titanium nitride). Ofcourse, it should be clear that the material of the insert 1 is notlimited to these materials.

Alternatively, the insert 1 may be configured to include a baseincluding the above material, and a coating layer that covers the base.Examples of material of the coating layer may include carbides,nitrides, oxides, oxocarbons, nitrogen oxides, carbonitrides andcarboxynitrides of titanium.

The coating layer may include one or a plurality of the above materials.The coating layer may be formed by one or a plurality of layerslaminated one upon another. The material of the coating layer is notlimited to the above materials.

The coating layer can be located on the base by using chemical vapordeposition (CVD) method or physical vapor deposition (PVD) method.

<Cutting Tools>

Cutting tools 101 in non-limiting embodiments of the present disclosuremay be described below with reference to the drawings.

The cutting tools 101 of the non-limiting embodiments may include aholder 103 and an insert 1. The holder 103 may have a bar shape.Alternatively, as illustrated in FIG. 11, the holder 103 may have aplate shape extended from a first end (lower right end in FIG. 11) to asecond end (upper left end in FIG. 11).

The holder 103 may include a pocket 105 located on a side of the firstend. As in an embodiment illustrated in FIG. 12, the holder 103 mayinclude an upper jaw 107 and a lower jaw 109 which are located on a sideof the first end and are located away from each other. The pocket 105may be formed by the upper jaw 107 and the lower jaw 109.

The insert 1 may be located in the pocket 105. In other words, theinsert 1 may be interposed between the upper jaw 107 and the lower jaw109. The insert 1 may be attached so that at least a part of a regionused as a cutting edge is protruded outward from the holder 103.

For example, steel and cast iron may be used as a material of the holder103. Of these materials, the use of steel may particularly contribute toenhancing toughness of the holder 103.

The cutting tool 101 for use in a so-called turning process may beillustrated in the embodiment illustrated in FIG. 11. The cutting tools101 in the non-limiting embodiments may be usable for a groovingprocess, but the use thereof is not limited thereto. There is no problemeven if the cutting tools 101 in the non-limiting embodiments are usedfor inner diameter process, outer diameter process and traversingprocess.

<Method for Manufacturing Machined Product>

Methods for manufacturing a machined product 201 in non-limitingembodiments may be described below with reference to the drawings.

The machined product 201 may be manufacturable by carrying out a cuttingprocess of a workpiece 203. The methods for manufacturing the machinedproduct 201 in the non-limiting embodiments may include the followingsteps:

(1) rotating the workpiece 203;

(2) bringing the cutting tool 101 represented by the above non-limitingembodiments into contact with the workpiece 203 being rotated; and

(3) moving the cutting tool 101 away from the workpiece 203.

More specifically, firstly, the workpiece 203 may be rotated around anaxis O2 as illustrated in FIG. 13, and the cutting tool 101 attached toa machine tool 301 may be relatively brought near the workpiece 203.Subsequently, the workpiece 203 may be cut out by bringing a ridgeline(cutting edge) in the cutting tool 101 into contact with the workpiece203 as illustrated in FIGS. 14 and 15. Thereafter, the cutting tool 101may be relatively moved away from the workpiece 203 as illustrated inFIG. 16.

In FIG. 13, the cutting tool 101 may be brought near the workpiece 203by moving the cutting tool 101 in a Y1 direction in a state where theaxis O2 is fixed and the workpiece 203 is rotated around the axis O2. InFIGS. 14 and 15, the workpiece 203 may be cut out by bringing thecutting edge in the insert 1 into contact with the workpiece 203 beingrotated. In FIG. 16, the cutting tool 101 may be moved away by movingthe cutting tool 101 in a Y2 direction in a state where the workpiece203 is rotated.

In the cutting process with the manufacturing method in the non-limitingembodiments, the cutting tool 101 may be brought into contact with theworkpiece 203, or the cutting tool 101 may be moved away from theworkpiece 203 by moving the cutting tool 101 in the individual steps.However, it is not intended to limit to this embodiment.

For example, the workpiece 203 may be brought near the cutting tool 101in the step (1). Similarly, the workpiece 203 may be moved away from thecutting tool 101 in the step (3). If it is desired to continue thecutting process, the step of bringing the cutting edge in the insert 1into contact with different portions of the workpiece 203 may berepeated while keeping the workpiece 203 rotated.

Representative examples of material of the workpiece 203 may includecarbon steel, alloy steel, stainless steel, cast iron or nonferrousmetals.

DESCRIPTION OF THE REFERENCE NUMERAL

-   -   1 insert    -   3 upper surface    -   5 lower surface    -   7 front lateral surface    -   9 rear lateral surface    -   11 first lateral surface    -   13 second lateral surface    -   15 first upper cutting edge    -   17 upper constraining surface    -   19 rake surface    -   21 second upper cutting edge    -   23 lower constraining surface    -   25 lower groove    -   27 inclined surface    -   27 a first inclined surface    -   27 b second inclined surface    -   29 concave curved surface    -   29 a first bottom part    -   29 b second bottom part    -   31 first region    -   33 second region    -   35 third region    -   37 first part    -   39 second part    -   41 upper groove    -   43 first portion    -   101 cutting tool    -   103 holder    -   105 pocket    -   107 upper jaw    -   109 lower jaw    -   201 machined product    -   203 workpiece    -   301 machine tool    -   O1 central axis    -   O2 axis    -   θ1 first angle    -   θ2 second angle    -   θ3 third angle    -   θ4 fourth angle    -   W1 first width    -   W2 second width    -   W3 third width    -   W4 fourth width

1. A cutting insert, comprising: an upper surface; a lower surfacelocated on a side opposite to the upper surface; a front lateral surfacelocated between the upper surface and the lower surface; and a rearlateral surface located between the upper surface and the lower surfaceand located on a side opposite to the front lateral surface, the uppersurface comprising a first upper cutting edge located on an intersectionwith the front lateral surface, and an upper constraining surface whichis located closer to the rear lateral surface than the first uppercutting edge and is contactable with a holder, the lower surfacecomprising a lower constraining surface contactable with the holder, thelower constraining surface comprising a lower groove having a V-shapeextended from a region located near the front lateral surface toward therear lateral surface, the lower groove comprising a first region locatedon a side opposite to the upper constraining surface, a second regionlocated closer to the front lateral surface than the first region, and athird region located closer to the rear lateral surface than the firstregion, wherein a wedge angle of the first region is a first angle, awedge angle of the second region is a second angle and a wedge angle ofthe third region is a third angle in a cross section orthogonal to anextending direction of the lower groove, and the first angle is smallerthan each of the second angle and the third angle.
 2. The cutting insertaccording to claim 1, wherein the second angle is smaller than the thirdangle.
 3. The cutting insert according to claim 1, wherein the upperconstraining surface comprises an upper groove having a V-shape extendedfrom a region located near the front lateral surface toward the rearlateral surface, and the upper groove is extended parallel to the lowergroove.
 4. The cutting insert according to claim 3, wherein a wedgeangle of the upper groove is a fourth angle in a cross sectionorthogonal to an extending direction of the upper groove, and the firstangle is smaller than the fourth angle.
 5. The cutting insert accordingto claim 4, wherein the third region comprises a first portion locatedon a side opposite to the upper constraining surface, and the thirdangle at the first portion is equal to the fourth angle.
 6. The cuttinginsert according to claim 1, wherein the first region comprises a firstbottom part having a concave curved surface shape, a first inclinedsurface that is flat and connects to the first bottom part along anextending direction of the lower groove, a width of the first bottompart in the extending direction of the lower groove is a first width,and a width of the first inclined surface in the extending direction ofthe lower groove is a second width, and a maximum value of the firstwidth is smaller than a maximum value of the second width.
 7. Thecutting insert according to claim 1, wherein the second region comprisesa second bottom part having a concave curved surface shape, and a secondinclined surface that is flat and connects to the second bottom partalong an extending direction of the lower groove, a width of the secondbottom part in the extending direction of the lower groove is a thirdwidth, and a width of the second inclined surface in the extendingdirection of the lower groove is a fourth width, and a maximum value ofthe third width is larger than a maximum value of the fourth width.
 8. Acutting tool, comprising: a holder which has a plate shape extended froma first end to a second end and comprises a pocket located on a side ofthe first end; and the cutting insert according to claim 1, the cuttinginsert being located in the pocket.
 9. A method for manufacturing amachined product, comprising: rotating a workpiece; bringing the cuttingtool according to claim 8 into contact with the workpiece being rotated;and moving the cutting tool away from the workpiece.